My pet hypothesis is that the US perspective is prescriptive, because the ability of the state to enforce the rights has not been seriously compromised in a long time. The rest of the world is more familiar with the idea that the guy with a bigger gun may one day show up and take your rights away.
In practice in the U.S. we pretty much call things 'rights' any time we believe that people should have them by default.
Positive freedom is a right to do something. (e.g. free speech) Negative freedom is a right to be free of something (e.g. violence)
Actually, it just occurred to me that free speech could be categorized as both: positive freedom to engage in speech and negative freedom to be free of government-based silence of that speech. Interesting.
Edit: I guess this is saying the same thing as 'User23 with so many words; "privileges and immunities" are probably better terms to use.